Eigenvalue estimate for the rough Laplacian on differential forms
Author(s)
Maerten, Daniel
Date issued
February 21, 2010
In
Manuscripta Math.
Vol
3-4
No
132
From page
399
To page
413
Subjects
Rough Laplacian eigenvalue estimate differential forms Weyl law
Abstract
We study the spectrum of the rough Laplacian acting on differential
forms on a compact Riemannian manifold (M,g).
We first construct on M metrics of volume 1 whose spectrum is as large as desired.
Then, provided that the Ricci curvature of g is bounded below,
we relate the spectrum of the rough Laplacian on 1--forms to the spectrum of the Laplacian on functions, and derive some upper bound in agreement with the asymptotic Weyl law.
forms on a compact Riemannian manifold (M,g).
We first construct on M metrics of volume 1 whose spectrum is as large as desired.
Then, provided that the Ricci curvature of g is bounded below,
we relate the spectrum of the rough Laplacian on 1--forms to the spectrum of the Laplacian on functions, and derive some upper bound in agreement with the asymptotic Weyl law.
Publication type
journal article